Probabilistic Reasoning by SAT Solvers

Abstract

In a series of papers we have shown that fundamental probabilistic reasoning problems can be encoded as hybrid probabilistic logic programs with probabilistic answer set semantics described in [24]. These probabilistic reasoning problems include, but not limited to, probabilistic planning [28], probabilistic planning with imperfect sensing actions [29], reinforcement learning [30], and Bayes reasoning [25]. Moreover, in [31] we also proved that stochastic satisfiability (SSAT) can be modularly encoded as hybrid probabilistic logic program with probabilistic answer set semantics, therefore, the applicability of SSAT to variety of fundamental probabilistic reasoning problems also carry over to hybrid probabilistic logic programs with probabilistic answer set semantics. The hybrid probabilistic logic programs encoding of these probabilistic reasoning problems is related to and can be translated into SAT, hence, state-of-the-art SAT solver can be used to solve these problems. This paper establishes the foundation of using SAT solvers for reasoning about variety of fundamental probabilistic reasoning problems. In this paper, we show that fundamental probabilistic reasoning problems that include probabilistic planning, probabilistic contingent planning, reinforcement learning, and Bayesian reasoning can be directly encoded as SAT formulae, hence state-of-the-art SAT solver can be used to solve these problems efficiently. We emphasize on SAT encoding for probabilistic planning and probabilistic contingent planning, as similar encoding carry over to reinforcement learning and Bayesian reasoning.